Mullins Effect and Crack Growth in Natural Rubber Vulcanizates during Heat Aging and Cyclic Loading

The effect of thermal aging and cyclic loading on mechanical properties and development of cracks in natural rubber vulcanizates was studied. After aging at 70oC and 110oC vulcanizates were subjected to cyclic loading. At a certain number of loading cycles, the samples were conducted in a tension test. At the aging condition of 70oC, the static tensile properties of material stay almost unchanged even after 88 aged hours and 8000 loading cycles. On the contrary, the dynamic fatigue resistance of vulcanizates decreases with increasing aging time. These results are attributed to the post-curing and the development of microcracks that might be caused by Mullins effect: in the case of static loading, the strain-induced crystallization may prevent cracks growth, but in the case of cyclic loading the strain-induced crystallization does not occur, so cracks develop without hindrance. However, at 110oC both static properties and dynamic fatigue resistance of material reduced dramatically because at high temperature the heat degradation exceeds both post-curing and strain-induced crystallization. Crack formation and propagation were examined by a digital optical microscope in the progress of cyclic loading. Results showed that natural rubber vulcanizate filled with carbon black has the best crack growth resistance (CGR) while the addition of modified and unmodified silica reduces CGR of materials. Moreover, the vulcanizate with unmodified silica has the lowest CGR.

Comparison of discontinuous damage models of Mullins-type

The Mullins effect is a characteristic property of filled rubber materials whose accurate and efficient modelling is still a challenging task. Innumerable constitutive models for elastomers are described in the literature. Therefore, this contribution gives a review on some widely used approaches, presents a classification, proves their thermodynamic consistency, and discusses reasonable modifications. To reduce the wide range of models, the choice is restricted to those which reproduce the idealised, discontinuous Mullins effect. Apart from the theoretical considerations, two compounds were produced and tested under cyclic uniaxial and equibiaxial tension as well as pure shear. Based on this experimental data, a benchmark that compares the fitting quality of the discussed models is compiled and favourable approaches are identified. The results are a sound basis for establishing novel or improving existing rubber models.

Anisotropic stress softening of residually stressed solids

Residual stress in purely elastic solids has been extensively studied in the literature. However, to the best of the author’s knowledge, the influence of residual stresses on anisotropic Mullins materials has not been studied. Hence, the aim of this paper is to propose an anisotropic phenomenological model to describe the Mullins phenomena for residually stressed elastomers; taking note that most materials are not purely elastic and some of them exhibit an anisotropic stress-softening phenomenon widely known as the Mullins effect. The anisotropic model is based on the use of direction-dependent damage parameters and a set of anisotropic spectral invariants presented recently in the literature by the author. The spectral invariants have a clear physical meaning that is useful in aiding the design of a rigorous experiment to construct a specific form of constitutive equation. Since boundary value results for residually stressed Mullins material are not found in the literature, the effect of residual stresses on the Mullins phenomena in simple tension, torsion and equibiaxial deformations is discussed in this paper.

The Influence of Filler Size and Crosslinking Degree of Polymers on Mullins Effect in Filled NR/BR Composites

Two factors, the crosslinking degree of the matrix (ν) and the size of the filler (Sz), have significant impact on the Mullins effect of filled elastomers. Herein, the result. of the two factors on Mullins effect is systematically investigated by adjusting the crosslinking degree of the matrix via adding maleic anhydride into a rubber matrix and controlling the particle size of the filler via ball milling. The dissipation ratios (the ratio of energy dissipation to input strain energy) of different filled natural rubber/butadiene rubber (NR/BR) elastomer composites are evaluated as a function of the maximum strain in cyclic loading (εm). The dissipation ratios show a linear relationship with the increase of εm within the test range, and they depend on the composite composition (ν and Sz). With the increase of ν, the dissipation ratios decrease with similar slope, and this is compared with the dissipation ratios increase which more steeply with the increase in Sz. This is further confirmed through a simulation that composites with larger particle size show a higher strain energy density when the strain level increases from 25% to 35%. The characteristic dependence of the dissipation ratios on ν and Sz is expected to reflect the Mullins effect with mathematical expression to improve engineering performance or prevent failure of rubber products.